Optical imaging systems comprising a plurality of rod lenses with a refractive index distribution in a radial direction that are arranged in an array are widely used in the image transmission portion of, for example, facsimile devices or copiers.
The refractive index distribution of such rod lenses can be expressed, for example by EQU n(r).sup.2 n=.sub.0.sup.2 .multidot.{1-(g.multidot.r).sup.2 +h.sub.4 .multidot.(g.multidot.r).sup.4 +h.sub.6 .multidot.(g.multidot.r).sup.6 }(Eq. 25)
wherein r is the radial distance from the optical axis of the rod lens, n(r) is the refractive index at the radial distance r from the optical axis of the rod lenses, n.sub.0 is the refractive index at the optical axis of the rod lens (center a refractive index), and g, h.sub.4 and h.sub.6 are coefficients for the refractive index distribution.
Conventionally, the resolving power demanded from such a rod lens array called for an MTF (modulation transfer function) of at least 60% when a pattern of 4-6 line-pairs/mm (ca. 200 dpi-300 dpi) was imaged. To meet this demand, it was sufficient to control only g or both g and h.sub.4 of the refractive index distribution coefficients for the rod lens.
Recently, however, with the steadily rising quality of printers and scanners, there is a demand for rod lens arrays with a resolving power of at least 12 line-pairs/mm (ca. 600 dpi). To realize a rod lens array having such a high resolving power, all refractive index distribution coefficients including h.sub.6 have to be controlled precisely during design and fabrication of the rod lens array.
It is possible to determine the optimum refractive index distribution coefficients for correcting the spherical aberration on the optical axis of a single rod lens. However, in the case of a plurality of rod lenses arranged in an array, not only spherical aberration, image curvature and astigmatism of the individual lenses, but also the overlapping of images from neighboring lenses may change the resolving power.
The optimum refractive index distribution changes also with the brightness of the rod lenses. For example, in the case of bright rod lenses with a large aperture angle, the refractive index distribution coefficients for a small axial spherical aberration are very different from the refractive index distribution coefficients for a small image curvature. The best resolving power can be attained by striking a balance between the two.
The overlapping degree is given by EQU m=X.sub.0 /2r.sub.0 (Eq. 26)
wherein r.sub.0 is the effective radius of the lens portion, that is the radius of the portion of the rod lenses that functions as a lens, and X.sub.0 is the image radius that a single rod lens projects onto the image plane (field of view). Here, X.sub.0 is defined as X.sub.0 =-r.sub.0 /cos(Z.sub.0 .pi./P), wherein Z.sub.0 is the rod lens length and P is the one-pitch length of the rod lens. Even if the rod lenses have the same refractive index distribution, the overlapping degree is dependent upon the length of the lenses, and thus changes the resolving power.
Consequently, to attain a high resolving power, the refractive index distribution coefficients have to be determined separately in accordance with at least the numerical angle and the overlapping degree of each rod lens.
The present invention has been developed with consideration of these facts. The purpose of the present invention is to provide an optical imaging system comprising a plurality of rod lenses arranged in an array, and having a refractive index distribution that is ideal for attaining a high resolving power.